Wiener transformation on functions with bounded averages

Abstract

The Wiener transformation (integrated Fourier transformation) on the space B 2 = { f : ‖ f ‖ = sup T ≥ 1 ( 1 2 T ∫ − T T | f | 2 ) 1 / 2 > ∞ } {B^2} = \{ f:\left \| f \right \| = {\sup _{T \geq 1}}{(\frac {1}{{2T}}{\int _{ - T}^T {\left | f \right |} ^2})^{1/2}} > \infty \} is studied.